Search

The non-first-order-factorizable contributions1 to the unpolarized and polarized massive operator matrix elements to three-loop order, AQg(3) and ΔAQg(3), are calculated in the single-mass case. For the F12-related master integrals of the problem, we use a semi-analytic method based on series expansions and utilize the first-order differential equations for the master integrals which does not need a special basis of the master integrals. Due to the singularity structure of this basis a part of the integrals has to be computed to O(ε5) in the dimensional parameter. The solutions have to be matched at a series of thresholds and pseudo-thresholds in the region of the Bjorken variable x∈]0,∞[ using highly precise series expansions to obtain the imaginary part of the physical amplitude for x∈]0,1] at a high relative accuracy. We compare the present results both with previous analytic results, the results for fixed Mellin moments, and a prediction in the small-x region. We also derive expansions in the region of small and large values of x. With this paper, all three-loop single-mass unpolarized and polarized operator matrix elements are calculated.

We consider light-fermion three-loop corrections to gg→HH using forward scattering kinematics in the limit of a vanishing Higgs boson mass, which covers a large part of the physical phase space. We compute the form factors and discuss the technical challenges. The approach outlined in this letter can be used to obtain the full virtual corrections to gg→HH at next-to-next-to-leading order.

We calculate the non-singlet, the pure singlet contribution, and their interference term, at O(α2) due to electron-pair initial state radiation to e+e− annihilation into a neutral vector boson in a direct analytic computation without any approximation. The correction is represented in terms of iterated incomplete elliptic integrals. Performing the limit s≫me2 we find discrepancies with the earlier results of Ref. [1] and confirm results obtained in Ref. [2] where the effective method of massive operator matrix elements has been used, which works for all but the power corrections in m2/s. In this way, we also confirm the validity of the factorization of massive partons in the Drell–Yan process. We also add non-logarithmic terms at O(α2) which have not been considered in [1]. The corrections are of central importance for precision analyses in e+e− annihilation into γ⁎/Z⁎ at high luminosity. Keywords: Higher order QED correction, e+e− annihilation, Precision physics at ILC, FCC, Iterated integrals

The QED initial state corrections are calculated to the forward–backward asymmetry for e+e−→γ⁎/Z0⁎ in the leading logarithmic approximation to O(α6L6), with L=ln⁡(s/me2), extending the known corrections up to O(α2L2) in analytic form. We use the method of massive on-shell operator matrix elements and present the radiators both in Mellin-N and momentum fraction z-space. Numerical results are presented for various energies around the Z-peak by also including energy cuts. These corrections are of relevance for the precision measurements at the FCC_ee.

We present numerical results on the recently completed O(α2) initial state corrections to the process e+e−→γ⁎/Z⁎, which is a central process at past and future high energy and high luminosity colliders for precision measurements of the properties of the Z-boson, the Higgs boson, and the top quark. We observe differences to an earlier result [1] in the non-logarithmic contributions at O(α2). The new result leads to a 4 MeV shift in the Z width considering the lower end s0=4mτ2 of the radiation region, which is larger than the present accuracy. A corresponding cut to s0/s=0.01 only implies a shift of 0.2 MeV. We present predictions on the radiative corrections to the central processes e+e−→γ⁎/Z⁎, e+e−→ZH and e+e−→tt‾ planned at future colliders like the ILC, CLIC, FCC_ee and CEPC to measure the mass and the width of the Z boson, the Higgs boson and the top quark, for which the present corrections are significant.

We present the matching relations of the variable flavor number scheme at next-to-leading order, which are of importance to define heavy quark partonic distributions for the use at high energy colliders such as Tevatron and the LHC. The consideration of the two-mass effects due to both charm and bottom quarks, having rather similar masses, are important. These effects have not been considered in previous investigations. Numerical results are presented for a wide range of scales. We also present the corresponding contributions to the structure function F2(x,Q2).